Internal problem ID [5932]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 68.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-\theta \left (-1+t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 39
dsolve([diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=Heaviside(t-1),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = -{\mathrm e}^{2 t}+{\mathrm e}^{3 t}-\frac {\theta \left (t -1\right ) {\mathrm e}^{2 t -2}}{2}+\frac {\theta \left (t -1\right ) {\mathrm e}^{3 t -3}}{3}+\frac {\theta \left (t -1\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 61
DSolve[{y''[t]-5*y'[t]+6*y[t]==UnitStep[t-1],{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} e^{2 t} \left (-1+e^t\right ) & t\leq 1 \\ \frac {e^3-3 e^{2 t} \left (e+2 e^3\right )+2 e^{3 t} \left (1+3 e^3\right )}{6 e^3} & \text {True} \\ \\ \\ \\ \\ \end{align*}